ELECTROCHEMISTRY - Wits Structural Chemistry

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Example 8 The limiting molar conductivities of KCl, KNO 3 , and AgNO 3 are 149,9, 145.0, and 133.4 S cm 2 mol -1 , respectively (all at 25 °C). What is the limiting molar conductivity of AgCl at this temperature To understand conductivity measurements, we need to understand why ions move at different rates Motion of ions is largely random, but in the presence of an electric field the motion is biased → migration DC, uniform electric field is applied Mobilities of Ions Electric field: ∆φ ε = ∆φ = potential difference = distance between electrodes ε = electric field V source + ∆φ + - Force acting on the ion due to electric field: ze∆φ ze = charge of ion F e = zeε = e = 1.602×10 -19 C causes ion to accelerate towards oppositely charge electrode. But ion undergoes frictional retardation when moving through the solvent: F Fric viscosity drag = fs = 6 πη as s = speed of ion η = viscosity of solvent a = radius of ion The two forces (one due to the electric field force and the other due to the viscosity drag, interactions between ions, etc.) act in the opposite directions. Eventually, these forces are balanced F e = F Fric and the ions reach a terminal speed called the drift speed. zeε = 6 πη as Self-study: What is the Grotthaus mechanism which is used to explain the very high mobility of H + in water zeε Drift speed: s = 6πη a stronger electric field ε faster ions drift s = uε u = ionic mobility = ze 6 πη a The drift speed governs the rate at which charge is transported. theoretical measurable LINK between mobility and molar conductivity ∴ expect the conductivity to decrease with increasing solution viscosity and increasing ion size. Ionic mobilities in water at 298 K, u /10 -8 m 2 s -1 V -1 H + 36.23 OH - 20.64 Na + 5.19 Cl - 7.91 K + 7.62 Br - 8.09 Zn 2+ 5.47 SO 2- 4 8.29 However, we see the larger ion (with the same charge) has a larger mobility. Need to consider: a = hydrodynamic radius i.e. includes hydration sphere Small ions are more extensively hydrated that larger ions (due to the stronger electric field) For cations and anions: λ = zuF And for very diluted solutions: o Λ m = ( ν+ z+ u+ + ν−z−u − )F Faraday’s constant = F = N A e Since Λ o m = ν+ λ+ +ν−λ− Ion-ion interactions affecting mobilities: In ionic solutions the ion-atmosphere also needs to be considered when ions migrate. When an electric field is introduced, two effects occur: Relaxation effect: When an electric field is introduced the ionic atmosphere is distorted as it drags behind moving charge. Central ion and atmosphere opposite in charge retardation of moving ion. Electrophoretic Effect: The ion-atmosphere moves in the opposite direction to the central ion which lead to the reduction in ion mobility. Both effects results in lower mobilities! Fick’s first law of diffusion: The flux (J) of particles is proportional to the concentration gradient. dc J = −D dx D = diffusion coefficient c = molar concentration x = distance Einstein equation: Stokes-Einstein equation: Nernst-Einstein equation: Applies to ions and uncharged particles in a solution. RT D = u zF Diffusion of Ions kT D = 6 πη a c 1 > c 2 c 1 c 2 J substitute expression for u k = Boltzmann constant = 1.381×10 -23 J K -1 Λ = F 2 o 2 ( ν+ z+ D+ + ν−z 2 Or for a m −D− ) λ+ = F 2 o ( ν + z 2 + D+ ) RT single ion: RT c Do Self-test 20.4 dc dx x 6
Fick’s second law of diffusion or the diffusion equation: 2 ∂c ∂ c = D 2 ∂t ∂x → describes time dependence of the diffusion process Diffusion coefficients at 298 K, 10 -9 m 2 s -1 Example 9 H + in water 9.31 The mobility of the NO 3- ion in aqueous solution at 25 °C is 7.40×10 -8 m 2 s -1 V -1 . Na + in water 1.33 (Viscosity of water is 0.89110 -3 kg m -1 s -1 ). sucrose in water 0.522 Calculate its diffusion coefficient and the effective radius at this temperature. It shows that the rate of change of conc is proportional to the curvature (the second derivative) of the concentration with respect to the distance. This equation shows that: 1) If the concentration changes sharply from point to point, then the concentration changes rapidly in time. c vs c x x 2) If the curvature = 0, then the concentration does not change in time. 3) If the concentration decreases linearly with distance, then the concentration is constant at any point, because the inflow is exactly balanced by the outflow of particles or ions. c x Remember: in the calculations you have to show the work on units. Without that, the work might be considered as not done at all. DYNAMIC <strong>ELECTROCHEMISTRY</strong> Double Layer at the Electrode-Solution Interface Dynamic Equilibrium Butler-Volmer Equation No Mass Transport Effects Mass Transport Effects Tafel Plot Electrolysis and Galvanic Cells Double Layer at the Electrode-Solution Interface Electrode reaction = heterogeneous chemical process e - ’s move from electrode surface to chemical species in solution (at the surface), or vice versa Diffusion layer – region dominated by unequal (1 µm − 1 mm) charge distribution Region of charge neutrality Part of Chapter 22 (1 − 10 nm) Double layer generated due to electrostatic forces Faradaic process: Helmholtz Model Gouy-Chapman Model Electrons transferred across the electrode-solution interface (reduction/oxidation) Governed by Faraday’s Law: current ∝ charge Non-Faradaic process: Under some conditions an electrodesolution interface shows a range of potentials where no charge transfer reaction occurs. E.g. capacitive or charging currents i Charging currents decay rapidly after applying a potential. t φ M + + + + + + + Electrode - - - - - - - Solution φ s Distance Double layer is like a capacitor 20-40 µF/cm 2 ∆φ = φ M - φ S = Galvani potential difference The potential difference between points in the bulk metal and the bulk solution. φ M Electrode OHP Solvated ions φ S φ M + + + + + + + Electrode Solution Distance Double layer has no thickness and is diffused by thermal motion of ions Stern Model φ M + + + + + + + Electrode - - - - - - - OHP rigid Helmholz plane Diffusion of charges caused by thermal motion of ions Distance 7
Page 1 and 2: ELECTROCHEMISTRY Mrs Billing GH840
Page 3 and 4: Standard Electrode Potentials The p
Page 5: Measuring the conductivity of tap w
Page 9 and 10: (1− α)nF ln j = ln jo + η RT Ta

ELECTROCHEMISTRY - Wits Structural Chemistry

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